Reactor Theory (Nuclear Parameters) DOE-HDBK-1019/2-93 NEUTRON LIFE CYCLE TABLE  1 Average  Number  of  Neutrons  Liberated in  Fission Fissile Nucleus Thermal Neutrons Fast Neutrons n h n h Uranium-233 2.49 2.29 2.58 2.40 Uranium-235 2.42 2.07 2.51 2.35 Plutonium-239 2.93 2.15 3.04 2.90 In the case where the fuel contains several fissionable materials, it is necessary to account for each material.   In the case of a reactor core containing both uranium-235 and uranium-238, the reproduction factor would be calculated as shown below. (3-2) h   N U  235 s U  235 f n U  235 N U  235 s U  235 a N U  238 s U  238 a Example: Calculate the reproduction factor for a reactor that uses 10% enriched uranium fuel.  The microscopic absorption cross section for uranium-235 is  694 barns.   The cross  section for uranium-238 is 2.71 barns.  The microscopic fission cross section for uranium-235 is 582 barns.  The atom density of uranium-235 is 4.83 x 10²¹ atoms/cm³.  The atom density of uranium-238 is 4.35 x 10²² atoms/cm³.   n is 2.42. Solution: Use Equation (3-2) to calculate the reproduction factor. h   N U  235 s U  235 f n U  235 N U  235 s U  235 a N U  238 s U  238 a                4.83  x  10²¹                 atoms cm³ 582  x  10 ²⁴cm² 2.42 4.83  x  10²¹ atoms cm³ 694  x  10 ²⁴cm²    4.35  x  10²²                 atoms cm³ 2.71  x  10 ²⁴cm² 1.96 Rev. 0 NP-03 Page 7